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ASTRONOMICAL DISCOVERIES OF NEWTON — COMBINED EXERTION NECESSARY FOR THE COMPLETION OF GREAT DISCOVERIES — SKETCH OF THE HISTORY OF ASTRONOMY PREVIOUS TO THE TIME OF NEWTON — DISCOVERIES OF NICOLAS COPERNICUS, BORN 1473, DIED 1553 — HE PLACES THE SUN IN THE CENTRE OF THE SYSTEM — HIS WORK ON THE REVOLUTIONS OF THE HEAVENLY BODIES, PRINTED AT THE EXPENSE OF CARDINAL SCHONBERG, AND DEDICATED TO POPE PAUL III. — TYCHO BRAHE, BORN 1546, DIED 1601 — HIS OBSERVATORY OF URANIBURG — IS VISITED BY JAMES VI. — IS PERSECUTED BY THE DANISH MINISTER — RETIRES TO GERMANY — HIS DISCOVERIES AND INSTRUMENTS — THE TYCHONIC SYSTEM — JOHN KEPLER, BORN 1571, DIED 1631 — his SPECULATION ON THE SIX REGULAR SOLIDS — DISCOVERS THE ELLIPTICITY OF MARS' ORBIT — HIS LAWS OF THE PLANETARY MOTIONS — HIS IDEAS OF GRAVITATION — HIS RELIGIOUS CHARACTER — GALILEO, BORN 1564, DIED 1642 — THE FIRST TO APPLY A TELESCOPE TO THE HEAVENS — DISCOVERS THE FOUR SATELLITES AND BELTS OF JUPITER — HIS RESEARCHES IN MECHANICS — IS SUMMONED BEFORE THE INQUISITION FOR HERESY — RETRACTS HIS OPINIONS, BUT PERSISTS IN TEACHING THE DOCTRINE OF THE EARTH'S MOTION — IS AGAIN SUMMONFD BEFORE THE INQUISITION — HIS SENTENCE TO IMPRISONMENT FOR LIFE — BECOMES BLIND — HIS SCIENTIFIC CHARACTER — LABOURS OF BOUILLAUD, AND OF BORELLI — SUGGESTIONS OF DR. HOOKE ON GRAVITY — HIS CIRCULAR PENDULUM — HIS EXPERIMENTS WITH IT — HIS VIEWS RESPECTING THE CAUSE OF THE PLANETARY MOTIONS.
From the optical researches of Newton, brilliant though they be, we turn with fresh wonder to the contemplation of his astronomical discoveries — those transcendent deductions of human reason, by which he has brightened the scientific glory of his country, achieved for himself an immortal name, and vindicated the intellectual dignity of his species. Pre-eminent as his triumphs have been, it would be unjust to affirm that they were won by his single arm. The torch of many a preceding age had thrown its light into the labyrinths of the material universe, and the grasp of many a powerful hand had thrown down the most impregnable of its barriers. An alliance indeed of many kindred spirits had been long struggling in the combat, and Newton was but the leader of the mighty phalanx — the director of their combined genius — the general who won the victory, and wears its laurels.
The history of science presents us with no example of an individual mind throwing itself far in advance of its contemporaries. It is only in his career of crime and ambition that reckless man takes the start of his species, and uncurbed by moral and religious ties, represses the claims of truth and justice, and founds an unholy empire upon the ruins of ancient and venerable institutions. The achievements of intellectual power, though frequently begun by one mind, and completed by another, have ever been the results of united labour. Slow in their growth, they gradually approximate to a more perfect condition: The variety in the objects and phenomena of nature, summons to research a variety of intellectual gifts : Observation collects her materials, and patiently plies her humble avocation : Experiment, with her quick eye and ready hand, develops new facts : The lofty powers of analysis and combination generalize insulated results, and establish physical laws; and in the ordeal of contending schools, and rival inquirers, truth is finally purified from error. How different is it with those systems which the imagination rears — those theories of wild import which are directed against the liberties, the consciences, and the hopes of man. The fatal poison tree distils its virus in the spring aswell as in the summer and the autumn of its growth; but the fruit which sustains life must have its bud prepared before the approach of winter, its blossom expanded in the spring, and its juice elaborated by the light and heat of a summer and an autumnal sun.
In the century which preceded the birth of Newton, the science of astronomy advanced with the most rapid pace. Emerging from the darkness of the middle ages, the human mind seemed to rejoice in its new-born strength, and to apply itself with elastic vigour to unfold the mechanism of the heavens. Ancient astronomers, indeed, had cleared and paved the way for the onward march of their science. A century and a half before Christ, Hipparchus, in his observatory at Rhodes, made the first catalogue of the stars, and representing the motions of the sun and moon by epicycles revolving upon circular orbits, he compiled tables for calculating their places in the heavens. Guided by the genius of Hipparchus, Claudius Ptolemy, a century and a half after Christ, though he placed the earth in the centre of the system, improved the theories of the sun, moon, and planets — discovered the principal inequality in the moon's orbi — -gave a theory of astronomical refractions more complete than that of any astronomer before Cassini, and bequeathed to posterity the valuable legacy of his Almagest, and his Five Books of Optics.
After centuries of darkness, Bagdad, the capital of Arabia, became the focus of science. The ancient astronomy was preserved and cultivated, but though new and more accurate observations were made, the science lay prostrate amid the cumbrous appendages of cycles and epicycles.<253>
In the thirteenth century, the noble-minded Alphonso X., sovereign of Castile, published, at a great expense, new astronomical tables, computed by the most distinguished professors in the Moorish universities; and, as if he had obtained a glimpse of a simpler arrangement, he denounced the rude mechanism of epicycles in language less reverent in its expression than in its truth. Were the heavens thus constituted, he said, I could have given the deity good advice had he consulted me at their creation. Notwithstanding these obstructions, Astronomy advanced, though with faltering steps, unable to escape from the trammels of authority, and free itself from those vulgar prejudices which a false interpretation of scripture had excited against a belief in the motion of the earth.
In this almost stationary condition, however, the science of the heavens was not suffered to remain. Nicolas Copernicus arose — a philosopher fitted to develop the true system of the universe, and a priest willing to give absolution for the sin of placing the great luminary in the centre of the system. This distinguished individual, a native of Thorn in Prussia, though of Bohemian origin, was born on the 19th January 1472. He at first followed his father's profession of medicine, but finding it uncongenial with his love of astronomy, he went to Bologna to study that science under Dominic Mario. In this situation he was less the disciple than the assistant and friend of Mario, and we find that he had made observations on the moon at that place in 1497. About the year 1500, he went to Rome, where he taught mathematics publicly to a large assemblage of youth, and of persons of distinction; and in the month of November of the same year, he observed an eclipse of the moon, and made other observations which formed the basis of his future researches. While thus occupied, thedeath of one of the Canons of the Cathedral Church of Ermeland, at Frauenburg, enabled his uncle, who was Bishop of that See, to nominate him to the vacant office. In this secluded spot, — in the residence of the Canons, situated on the brow of a hill, Copernicus carried on his astronomical observations. During his sojourn at Rome, the Bishop of Fossombrossa, who presided over the council for reforming the calendar, had requested his assistance in that important undertaking. Upon this congenial task he entered with youthful zeal. He charged himself with the duty of determining the length of the year, and the other elements which were required by the council; but the observations became irksome, and interfered with the completion of those interesting views which had already dawned upon his mind.
Convinced that the simplicity and harmony which appeared in the other works of creation should characterize the arrangements of the planetary system, he could not regard the hypothesis of Ptolemy as a representation of nature. This opinion was strengthened by actual observation. The variable appearance of the superior planets, of Mars, for example, in opposition and conjunction, — in the one case shining with the effulgence of Jupiter, and in the other with the light of a secondary star, was irreconcilable with the dogma that the planet moved round the earth. That it moved round the sun was the conclusion to which he was then led; and the grand idea of the bright orb of day being the centre of the planetary system burst upon his mind, though perhaps with all the dimness of a dream — the first phase of every great discovery. In the opinions of the Egyptian sages, — in those of Pythagoras, Philolaus, Aristarchus, and Nicetas of Syracuse, he recognised his first conviction that the earthwas not the centre of the universe; and in the works of Martianus Capella, he found it to be the opinion of the Egyptians that Mercury and Venus revolved about the sun during his annual motion round the earth. Thus confirmed in his views, the difficulties which had previously surrounded them were gradually dispelled, and after thirty-six years of intense study, in which the labours of the observer, and the calculations of the mathematician, were combined with the sagacity of the philosopher, he was permitted to develop the true system of the heavens.
In his eye the sun stood immovable in the centre of the universe, while the earth revolved annually round him between the orbits of Venus and Mars, producing by its rotation upon its axis in twenty-four hours all the diurnal phenomena of the celestial sphere — Mercury and Venus revolving round the sun within the earth's orbit, and all the rest of the planets without it, while the moon revolved monthly round the earth during its annual motion. In the system thus constituted, all the phenomena of the celestial motions received an immediate explanation. The alternation of day and night — the vicissitudes of the seasons — the varying brightness of the planets — their stations and retrogradations, and even the precession of the Equinoxes, became the necessary results of the Copernican System.
The circulation of these great truths, and of the principles on which they rest, became the leading object of Copernicus's life. The Canon of Ermeland, however, saw the difficulties of his position, and exhibited the most consummate prudence in surmounting them. Aware of the prejudice and even of the hostility with which his discoveries would be received, he resolved neither to startle the one nor provoke the other. He committed maticians, and I am much mistaken if such men will not regard my labours as conducive to the prosperity of the ecclesiastical republic over which your Holiness presides." Thus recommended to the sovereign authority of the Church, and vindicated against the charge of being hostile to Scripture, the Copernican system met with no ecclesiastical opposition, and gradually made its way in spite of the ignorance and prejudices of the age.his opinions to the slow current of personal communication. The points of opposition which they presented to received doctrine were thus gradually worn down, and they insinuated themselves into ecclesiastical minds by the very reluctance of their author to bring them into notice. In 1536, Cardinal Nicolas Schonberg, Bishop of Capua, and Tidemann Gyse, Bishop of Culm, exerted all their influence to induce Copernicus to lay his system before the world; but their entreaties were in vain, and it was not published till 1539, when an accidental circumstance, contributed with other causes to alter his resolution. Having heard of the system of Copernicus, George Rheticus, Professor of Mathematics at Wirtemberg, resigned his chair, and repaired to Frauenburg to make himself master of his discoveries. After studying and adopting them, this zealous disciple prevailed upon Copernicus to permit their publication; and they seemed to have arranged a plan for giving them to the world without alarming the vigilance of the Church. Under the disguise of a student of mathematics, Rheticus published in 1540 an account of the manuscript volume of Copernicus. The pamphlet was received without any expression of censure, and its author was thus encouraged to reprint it at Basle with his own name. The success of these publications, and the flattering manner in which the new astronomy was received, combined with the solicitations and even reproaches of his friends, overcame the scruples of Copernicus, and induced him to place his manuscript in the hands of Rheticus. It was accordingly printed at the expense of Cardinal Schonberg, and was published at Nuremberg in 1543, under the title of "On the Revolutions of the Celestial Bodies." Its illustrious author, however, did not live to peruse it. A complete copy was handed to him on his dying day, and he saw and touched it a few hours before he expired. In an introductory address "on the hypotheses of his work," Copernicus propitiates such of his readers as may be alarmed at their novelty, by assuring them that it is not necessary that astronomical hypotheses be either true or probable, and that they accomplish their object if they reconcile the calculus with observation. With the same view he inscribed his preface to the Holy Pontiff himself, and boldly alludes to the hostility to which his opinions will expose him. "I have preferred," says he, "dedicating my lucubrations to your Holiness rather than to any other person, because, in the very remote corner of the world in which I live, you are so distinguished by your rank and your love of learning and mathematics, that you will easily repress the virulence of slander, notwithstanding the proverb that there is no remedy against the wound of the sycophant." And "should there be any babblers who, ignorant of all mathematics, presume to judge of these things, on account of some passage of scripture wrested to their own purpose, and dare to blame and cavil at my work, I will not scruple to hold their judgment in contempt. . . . . Mathematics are written for mathe
Although the true solar system was thus established, yet much remained to be done by the practical astronomer before the motions of the planets could be subjected to mechanical laws. Copernicus had not rejected the machinery of epicycles; and the distances of the planets and the form of their orbits, were very imperfectly known. A skilful observer, therefore, expert in mechanism, and girt for nocturnal labour, was now required to prepare for Kepler distances and periods, and for Newton the raw material of his philosophy.
The astronomer thus required appeared in the person of Tycho Brahe, who was born at Knudstrup, in Scania, on the 14th December 1546, three years after the death of Copernicus. When a student at Copenhagen, the great solar eclipse of the 21st August 1560 arrested his attention, and having found that all its phases had been accurately predicted, he resolved to acquire the knowledge of a science so infallible in its results. Though destined for the profession of the law, he refused to enter upon its study; and when urged to it by the entreaties and reproaches of his friends, he escaped from their importunities by travelling into Germany. During his visit to Augsburg, he resided in the house of Peter Hainzell, the burgomaster, whom he inspired with such a love of astronomy, that he erected an excellent observatory athis own expense, and thus enabled his youthful instructor to commence that splendid career of observation which has placed him in the first rank of practical astronomers.
On his return to Copenhagen in 1570, he was welcomed by the King and the nobility as an honour to the nation, and his maternal uncle at Herritzvold, near his native place, offered him a retreat from the gaieties of the capital, and every accommodation for pursuing his astronomical studies. Love and alchemy, however, distracted his thoughts; but he found the peasant girl, whom he fancied, of easier attainment than the philosopher's stone. His noble relatives were deeply offended with the marriage, and it required all the influence of the King to allay the quarrel which it occasioned. In 1572 and 1573, he had observed the remarkable star in Cassiopeia, which rivalled Venus in her greatest brightness, and which, after being the wonder of astronomers for sixteen months, disappeared in March 1574; but he refused, for a long time, to publish his observations upon it, lest he should thus cast a stain upon his nobility!
Fickle in purpose, and discontented with Denmark, Tycho set out in search of a more suitable residence; but when the King heard of his plans, he resolved to detain him by acts of kindness and liberality. He was therefore presented to the canonry of Roschild, with an annual income of 2000 crowns, and an additional pension of 1000; and the island of Huen was offered to him as the site of an observatory, to be furnished with instruments of his own choice. The generous offer was instantly accepted. The celebrated observatory of Uraniburg — the city of the Heavens — was completed at the expense of £20,000, and from its hallowed towers Tycho continued for twenty-one years to enrich astronomy with the most valuableobservations. From every kingdom in Europe admiring disciples repaired to this sanctuary of the sciences, to acquire a knowledge of the heavens; and kings and princes felt themselves honoured as the guests of the great astronomer.
Among the princes who visited Uraniburg, we are proud to enumerate James VI. of Scotland. In 1590, during his visit to Denmark to celebrate his marriage with the Princess Anne, he spent eight days with Tycho, accompanied by his counsellors and a large suite of nobility. He studied the construction and use of the astronomical instruments; he inspected the busts and pictures in the Museum, and when he found among them the portrait of his own distinguished preceptor, George Buchanan, he could not refrain from the strongest expressions of delight. Upon quitting Uraniburg, James not only presented Tycho with a magnificent donation, but afterwards gave him his Royal license to publish his works in England.
The equanimity of Tycho was not disturbed by these marks of respect and admiration; but while they animated his zeal and stimulated his labours, they were destined to be the instruments of his ruin. By the death of Frederick II. in 1588, Tycho lost his most valued friend; and though his son and successor, Christian IV., visited Uraniburg, and seemed to take an interest in astronomy, his wishes to foster it, if he did cherish them, must have been overruled by the influence of his counsellors. The parasites of royalty found themselves eclipsed by the brightness of Tycho's reputation. They envied the munificent provision which Frederick had made for him; and instigated by a physician who was jealous of his reputation, as a successful practitioner of medicine, they succeeded in exciting against Tycho the hostility of the court. Walchendorp, the President of the Council, was the tool of his enemies, and on the ground of an exhausted treasury, and the inutility of the studies of Tycho, he was deprived of his canonry, his pension, and his Norwegian estate.
Thus stripped of his income and degraded from his office, Tycho, with his wife and family, sought for shelter in a foreign land. His friend, Count Henry Rantzau, offered him the hospitality of his Castle of Wandesberg, near Hamburg, and having embarked his family and his instruments on board a small vessel, the exiled patriarch left his ungrateful country never to return. In the Castle of Wandesberg he enjoyed the kindness and conversation of his accomplished host, by whom he was introduced to the Emperor Rodolph, who, to a love of science, added a passion for alchemy and astrology. The reputation of Tycho having already reached the Imperial ear, the recommendation of Rantzau was hardly necessary to insure him his warmest friendship. On the invitation of the Emperor, he repaired in 1599 to Prague, where he met with the kindest reception. A pension of 3000 crowns was immediately settled upon him, and a commodious observatory erected for his use. Here he renewed with delight his interrupted labours, and rejoiced in the resting-place which he had so unexpectedly found for his approaching infirmities. These prospects of returning prosperity were enhanced by the pleasure of receiving into his house two such pupils as Kepler and Longomontanus; but the fallacy of human anticipations was here, as in so many other cases, strikingly displayed. His toils and his disappointments had made severe inroads upon his constitution. Though surrounded with affectionate friends and admiring disciples, he was still an exile in a foreign land. Though his country had been base in its ingratitude, it was yet the land which he loved, — the scene of his earliest affections, — the theatre of his scientific glory. These feelings constantly preyed upon his mind, and his unsettled spirit was ever hovering among his native mountains. In this condition he was attacked with a disease of the most painful kind, and though the paroxysms of its agonies had lengthened intermissions, yet he saw that death was approaching him. He implored his pupils to persevere in their scientific labours. He conversed with Kepler on some of the profoundest questions in astronomy, and with these secular occupations he mingled frequent acts of piety and devotion. In this happy frame of mind he expired without pain on the 24th October 1601, at the age of fifty-five, the unquestionable victim of the councils of Christian IV.
Among the great discoveries of Tycho, his improvements of the lunar theory are perhaps the most important. He discovered the inequality, called the variation, amounting to thirty-seven minutes, and depending on the distance of the moon from the sun. He discovered also the annual inequality of the moon depending on the position of the earth in its orbit, and affecting also the place of her apogee and node. He determined likewise the greatest and the least inclination of the moon's orbit, and he represented this variation by the motion of the pole of the orbit in a small circle. Tycho had the merit, too, of being the first to correct by the refraction of the atmosphere the apparent places of the heavenly bodies; but, what is very unaccountable, he made the refraction which he found to be 34′ in the horizon, to vanish at 45°, and he maintained that the light of the moon and stars was refracted differently by the atmosphere! By his observations on the comet of 1577 he proved that it was three times as A.D. — a catalogue afterwards enlarged by Kepler from Tycho's observations, and published in 1627. The skill of Tycho in observing phenomena, surpassed his genius for discovering their cause, and it was perhaps from his veneration for the Scriptures, rather than from the vanity of giving his name to a new system, that he rejected the Copernicus hypothesis. In the system which bears his name, the earth is stationary in the centre of the universe, while the sun with all the other planets and comets revolving around him, performs his daily revolution about the earth.distant as the moon, and that since these bodies moved in all directions, the doctrine of solid orbs could not be true. By means of large and accurately divided instruments, some of which were altitude and azimuth ones, having their divided circles six and nine feet in diameter, and others mural quadrants, sextants, and armillary spheres, he made a vast collection of observations, which led Kepler to the discovery of his celebrated laws, and formed the basis of the Rudolphine Tables. But the most laborious of his undertakings was his catalogue of 777 stars, for the epoch of 1600,
Notwithstanding the great accessions which astronomy had received from Copernicus and Tycho, yet no progress had been made in developing the general laws of the Solar System, and scarcely an idea had been formed of the invisible power by which the planets were retained in their orbits. The materials, however, were prepared, and Kepler arose to lay the foundations of a structure which Newton was destined to complete.
John Kepler was born at the imperial city of Wiel, in Wirtemberg, on the 21st December 1571. Although hisearly education was neglected, he made considerable progress in his studies at the preparatory school of Maulbronn, and when he took his degree of Master of Arts at the University of Tübingen in 1591, he held the second place at the examination. While he was the mathematical pupil of Mæstlin, he not only adopted his views of the Copernican System, but wrote an essay on the "Primary Motion," as produced by the earth's daily rotation. When the astronomical chair at Gratz, in Styria, fell vacant in 1594, Kepler accepted the appointment, although he knew little of mathematics. His attention, however, was necessarily turned to astronomy, and in 1595, when he enjoyed some professional leisure, he directed the whole energy of his mind to the number, the dimensions, and the motions of the orbits of the planets. After various fruitless attempts to discover some relation between the distances and magnitude of the planets, by assuming the existence of new planets in the wider spaces, he at last conceived the extraordinary idea that the distances of the planets were regulated by the six regular geometrical solids. "The Earth's orbit," says he, "is the sphere, the measurer of all. Round it describe a dodecahedron, the circle including this will be (the orbit of) Mars. Round Mars describe a tetrahedron, the circle including this will be Jupiter. Describe a cube round Jupiter, the circle including this will be Saturn. Then inscribe in the (orbit of the) Earth an icosahedron, the circle described in it will be Venus. Describe an octahedron round Venus, the circle inscribed in it will be Mercury. This singular law, rudely harmonizing with some of Copernicus's measures, would have failed, for want of solids, in its application to Uranus and Neptune; but it took possession of Kepler's mind, and he declared that he would not barter the glory of its invention for the whole Electorate of Saxony." When Galileo's opinion of this hypothesis was requested by Kepler, he praised the ingenuity which it displayed; but when a copy of the Prodromus was presented to Tycho, he advised his young friend "first to lay a solid foundation for his views by actual observation, and by ascending from these to strive to reach the causes of things;" and there is reason to believe, that by the magic of the whole Baconian philosophy thus compressed by anticipation into a nutshell, Kepler abandoned for a while his visionary speculations.
When driven by religious persecution from the states of Styria, he accepted an invitation from Tycho to settle at Prague as his assistant. Here he was introduced to the Emperor Rodolph, and upon Tycho's death in 1601, he was appointed mathematician to the Emperor, a situation which he held during the successive reigns of Matthias and Ferdinand.
After devoting much of his time to the subjects of refraction and vision, and adding largely to our knowledge of both these branches of optics, he resumed his inquiries respecting the orbits of the planets. Possessed of the numerous and valuable observations of Tycho, he endeavoured to represent them by the hypothesis of a uniform motion in circular orbits; but in examining the orbit of Mars, he found the deviations from a circle too great to be owing to errors of observation. He therefore compared the observations with various other curves, andwas led to the fine discovery that Mars revolved round the sun in an elliptical orbit in one of the foci of which the sun himself was placed. By means of the same observations he computed the dimensions of the planet's orbit, and by comparing the times in which Mars passed over different parts of it, he found that they were to one another as the areas described by the lines drawn from the centre of the planet to the centre of the sun, or, in more technical language, that the radius vector, or line joining the sun and planet, describes equal areas in equal times. These two brilliant discoveries, the first ever made in physical astronomy, were extended to all the other planets of the system, and were given to the world in his Commentaries on the Motions of the Planet Mars.
Thus successful in his researches, and overjoyed with the result of them, Kepler renewed his attempts to discover the mysterious relation which he believed to exist between the mean distances of the planets from the sun. Distrusting his original hypothesis of the geometrical solids, he compared the planetary distances with the intervals of musical notes, but though he was supported in this notion by the opinions of Pythagoras, and even of Archimedes, his comparisons were fruitless, and he was about to abandon all inquiry which had more or less occupied his mind during seventeen years of his life.
After Kepler had refused to accept the mathematical chair at Bologna, which was offered to him in 1617, he seems to have resumed his speculations "on the exquisite harmonies of the celestial motions." On the 8th March 1618, he conceived the idea of comparing the powers ofthe different numbers which express the distances of the planets, with the powers of the different numbers which express their periods round the sun. He compared, for example, the squares and the cubes of the distances with the same powers of the periodic times, and he even made the comparison between the squares of the periodic times and the cubes of the distances; but having, in the hurry and impatience of research, been led into an error of calculation, he rejected the last of these relations, — the relation that was true, — as having no existence in nature. Before a week, however, had elapsed, his mind reverted to the law which he had rejected, and, upon repeating his calculations, and discovering his error, he recognised with rapture the great truth of which he had for seventeen years been in search, that the periodic times of any two planets in the system are to one another as the cubes of their distances from the sun. This discovery was published in 1619 in his "Harmony of the World," which was dedicated to James VI. of Scotland, and which is marked with all the peculiarities of the author. The passage which describes the feelings under which he recognised the truth of his third law, is too instructive to be omitted from his history : — " What sixteen years ago I urged as a thing to be sought — that for which I joined Tycho Brahe — for which I settled in Prague — for which I have devoted the best part of my life to astronomical contemplations — at length I have brought to light, and have recognised its truth beyond my most sanguine expectations. . . . . It is now eighteen months since I got the first glimpse of light, three months since the dawn; a very few days since the unveiled sun, most admirable to gaze on, burst out upon me . . . . the die is cast — the book is written, to be read either now or by posterity, I care not which. It may well wait a century for a reader, as God has waited six thousand years for an interpreter of his works."
As the planes of the orbits of all the planets, as well as the line of their apsides passed through the sun, Kepler could not fail to suspect that some power resided in that luminary, by which the motions of the planets were produced, and he went so far as to conjecture that this power diminishes as the square of the distance of the body on which it was exerted; but he immediately rejects this law in favour of that of the simple distances. In the Introduction to his Commentaries on Mars, he distinctly recognises the mutual gravitation of matter, in the descent of heavy bodies to the centre of the earth, as the centre of a round body of the same nature with themselves. He maintained, that two stones situated beyond the influence of a third body would approach like two magnets, and meet at a point, each describing a space proportional to the mass of the other. He maintained also, that the tides were occasioned by the moon's attraction, and that the lunar inequalities were owing to the joint action of the sun and earth. Our countryman, Dr. Gilbert, in his celebrated book De Magnete, published in 1600, had about the same time announced similar opinions on gravitation. He compares the earth's action upon the moon to that of a great loadstone; and in his posthumous work which appeared half a century afterwards, he maintains that the earth and moon act upon each other like two magnets, the influence of the earth being the greater on account of its superior mass. But though these opinions were a step in celestial physics, yet the identity of thegravity which is exhibited on the earth's surface by falling bodies, with that which guided the planets in their orbits, was not revealed either to the English or the German philosopher. It required more patience and thought than either could command, and its discovery was reserved for the exercise of higher powers.
The misery in which Kepler lived, stands in painful contrast with his arduous labours as an author, and his noble services to science. His small pension was ever in arrears, and when he retired to Silesia to spend the remainder of his days in retirement, his pecuniary difficulties became more embarrassing than before. He was compelled to apply personally for his arrears; and, in consequence of the great fatigue which he suffered in his long journey to Ratisbon on horseback, he was seized with a fever which carried him off on the 30th November 1630, in the fifty-ninth year of his age. Thus perished one of the noblest of his race, a victim of poverty, and a martyr to science.
In a work which is to record the religious character of Newton, it would be unjust to withhold from Kepler the credit which is due to his piety and faith. The harmony of the universe, which he strove to expound, excited in him not only admiration, but love. He felt his own humility the farther he penetrated into the mysteries of the universe, and sensible of the incompetency of his unaided powers for such transcendent researches, and recognising himself as but the instrument of the Almighty in making known his wonders, he never entered upon an inquiry without praying for assistance from above. Nor was this frame of mind inconsistent with the tumultuous delight with which he surveyed his discoveries. His was the unpretending ovation of success, not the ostentatious triumphof ambition; and if a noble pride occasionally mingled with his feelings, it was the pride of being the chosen messenger of physical truth, not the vanity of being the favoured possessor of superior genius. With such a frame of mind, Kepler was necessarily a Christian. The afflictions with which he was tried confirmed his faith and brightened his hopes. He bore them in all their variety and severity with Christian patience; and though he knew that this world was to be the theatre of his glory, yet he felt that his rest and his reward could be found only in another.
It is a remarkable fact in the history of astronomy, that three of its most distinguished cultivators were contemporaries. Galileo was the contemporary of Tycho during thirty-seven years, and of Kepler during the fifty-nine years of his life. Galileo was born seven years before Kepler, and survived him nearly the same time. We have not learned that the intellectual triumvirate of the age enjoyed any opportunity for mutual congratulation. What a privilege would it have been to have contrasted the aristocratic dignity of Tycho with the reckless ease of Kepler, and the manly and impetuous mien of the Italian sage!
While his two predecessors were laying deeply and surely the foundations of physical astronomy, Galileo was preparing himself for extending widely the limits of the Solar system, and exploring the structure of the bodies that compose it. He was born at Pisa on the 15th February 1564, and was descended from the noble family of Bonajuti. Although he exhibited an early passion for geometry, and had studied without a master the writings of Euclid and Archimedes, yet even after he was called to the mathematical chair at Pisa in the twenty-fifth year ofhis age, he was more distinguished for his hostility to the Aristotelian philosophy than for his progress in original inquiry. In 1592 he was promoted to the same chair in Padua, where he remained for eighteen years, adorning the university by his talents, and diffusing around him a taste for science. With the exception of some minor contrivances, Galileo had made no discovery till he entered his forty-fifth year, an age at which Newton had completed all his discoveries. In 1609, the memorable year in which Kepler published his "New Astronomy," Galileo paid that visit to Venice during which he beard of the telescope of Lippershey. The idea of so extraordinary an instrument at once filled his mind, and when he learned from Paris that it had an existence, he resolved instantly to realize it. The simple idea, indeed, was the invention, and Galileo's knowledge of optics was sufficient to satisfy him that a convex lens at one end of a tube, with a concave one at the other, would bring objects nearer to his eye. The lenses were placed in the tube, the astronomer looked into the concave lens, and saw the objects before it "pretty large and pretty near him." This little toy, which magnified only three times lineally, and nine times superficially, he carried in triumph to Venice, where the chief magistrate obtained it in barter for the life possession of his professorship, and 480 florins as an increase of salary. The excitement produced on this occasion at Venice was of the most extraordinary kind; and, on a subsequent occasion, when Sirturi had made one of the instruments, the populace followed him with eager curiosity, and at last took possession of the tube, till they had each witnessed its wondrous effects. Galileo lost no time in availing himself of his new power. He made another telescope which magnified about eight or nine times, and, sparing neither labour nor expense, he finally constructed an instrument so excellent, as "to show things almost a thousand times larger, (in surface,) and above thirty times nearer to the eye."
There is, perhaps, no invention in science so extraordinary in its nature, and so boundless in its influence, as that of the telescope. To the uneducated man the power of bringing distant objects near to the eye must seem almost miraculous; and to the philosopher even who comprehends the principles upon which it acts, it must ever appear one of the most elegant applications of science. To have been the first astronomer in whose hands such a power was placed, was a preference to which Galileo owed much of his reputation.
Before the telescope was directed to the heavens, it was impossible to distinguish a planet from a star. Even with his first instrument, Galileo saw that Jupiter had a round appearance like the sun and moon; but, on the 7th January 1610, when he used a telescope of superior power, he saw two little bright stars very near him, two to the right, and one to the left of his disc. Though ranged in a line parallel to the ecliptic, he regarded them as ordinary stars; but having, on the 8th of January, accidentally directed his telescope to Jupiter, he was surprised to see the three stars to the west of the planet, and nearer one another than before, — a proof that they had a motion of their own. This fact did not excite his notice; and it was only after observing various changes in their relative position, and discovering a fourth onthe 13th of January, that he was enabled to announce the discovery of the four satellites of Jupiter.
In continuing his observations with the telescope, Galileo discovered that Venus had the same crescent phases as the waxing and the waning moon; — that the sun had spots on his surface which proved that he revolved round his axis; — that Saturn was not round, but had handles attached to his disc; — that the surface of the moon was covered with mountains and valleys, and that parts of the margin of her disc occasionally appeared and disappeared; — that the milky-way consisted of numerous stars, which the unassisted eye was unable to perceive; and that the apparent size of the stars arose from irradiation, or a spurious light, in consequence of which they were not magnified by the telescope. These various discoveries furnished new arguments in support of the hypothesis of Copernicus; and we may now consider it as established by incontrovertible evidence, which ignorance or fanaticism only could resist, that the sun is placed in the centre of the System, in the focus of the elliptical, or in the centre of the circular orbits of the planets, and that by some power yet to be discovered, he guides them in their course, while the Earth and Jupiter exercise a similar influence over the satellites which accompany them.
But it is not merely from his astronomical discoveries, brilliant as they are, that Galileo claims a high place in the history of Newton's discoveries. His profound researches on mechanical science — his determination of the law of acceleration in falling bodies — and his researches respecting the resistance and cohesion of solid bodies, the motion of projectiles, and the centre of gravity of solids,have ranked him among the most distinguished of our mechanical philosophers. The great step, however, which he made in mechanics, was his discovery of the general laws of motion uniformly accelerated, which may be regarded as the basis of the theory of universal gravitation.
The current of Galileo's life had hitherto flowed in a smooth and undisturbed channel. His discoveries had placed him at the head of the great men of the age, and with an income above his wants, he possessed both the means and the leisure for prosecuting his studies. Anxious, however, to propagate the great truths which he discovered, and by force of reason to make proselytes of his enemies, he involved himself in disputes which tried his temper and disturbed his peace. When argument failed to convince his opponents, he wielded against them the powerful weapons of ridicule and sarcasm, and he had thus marshalled against himself and his opinions, the Aristotelian professors, the temporizing Jesuits, the political churchmen, and that timid section of the community who tremble at innovation, whether it be in religion or in science. The party of Galileo who abetted him in his crusade against error, though weak in numbers, were strong in position and in zeal. His numerous pupils occupying the principal chairs in the Italian universities, formed a devoted band who cherished his doctrines and idolized his genius. The enemies of religion followed the intellectual banner, and many princes and nobles, who had smarted under ecclesiastical jurisdiction, were willing to see it shorn of its power.
While these two parties were standing on the defensive, Galileo hoisted the first signal for war. In a letter to his friend and pupil, the Abbé Castelli, he proved that the Scriptures were not intended to teach us science and philosophy, and that the expressions in the Bible were as irreconcilable with the Ptolemaic as with the Copernican system. In reply to this letter, Caccini, a Dominican friar, attacked Galileo from the pulpit, and so violent was his language, that Maraffi, the general of the Dominicans, expressed his regret that he should be implicated "in the brutal conduct of thirty or forty thousand monks." Encouraged by this apology, Galileo launched another pamphlet, addressed to the Grand Duchess of Tuscany, in which he supports his views by quotations from the Fathers, and by the conduct of the Roman Pontiff himself, Paul III., in accepting the dedication of Copernicus's work. It was in vain to meet such arguments by any other weapon than that of the civil power. It was deemed necessary either to crush the heresy, or retire from the contest; and the church party determined to appeal to the Inquisition.
Various circumstances concurred to excite the suspicions of Galileo, and, about the end of 1615, he set off for Rome, where he was lodged in the palace of the Tuscan ambassador. While Galileo was enjoying the hospitality of his friend, Caccini was preparing the evidence of his heresy, and in due time he was charged by the Inquisition with maintaining the motion of the earth and the stability of the sun, — with teaching and publishing this heretical doctrine, and with attempting to reconcile it to Scripture. On the 25th February 1615, the Inquisition assembled to take these charges into consideration, and having no doubt of their truth, they desired that Galileo should be enjoined by Cardinal Bellarmine to renounce the obnoxious doctrines, and to pledge himself that he would neither teach, publish, nor defend them in future. In the event of his refusing to obey this injunction, it was decreed that he should be thrown into prison. Galileo acquiesced in the sentence, and on the following day he renounced before the Cardinal his heretical opinions, abandoning the doctrine of the earth's motion, and pledging himself neither to defend nor teach it either in his writings or his conversation.
Although Galileo had made a narrow escape from the grasp of the Inquisition, he left home in 1616 with a suppressed hostility against the church; and his resolution to propagate the heresy seems to have been coeval with the vow by which he renounced it. Although he affected to bow to the decisions of theology, he never scrupled, either in his writings or in his conversation, to denounce them with the severest invective. The Lyncean Academy, ever hostile to the church, encouraged him in this unwise procedure, and it was doubtless at their instigation that he took the daring step which brought him a second time to the bar of the Inquisition. Forgetting the pledges under which he lay, — the personal kindness of the Pope, — and the pecuniary obligations which he owed him, he resolved to compose a work in which the Copernican system should be indirectly demonstrated. This work, entitled, The System of the World of Galileo Galilei, &c., was completed in 1630, but was not published till 1632, owing to the difficulty of obtaining a license to print it. It was dedicated to the Grand Duke of Tuscany; and while the decree of the Inquisition was referred to in insulting and ironical language, the Ptolemaic system, the doctrine of the Church, was assailed by arguments which admitted of no reply. The Copernicandoctrines, thus eloquently maintained, were eagerly received and widely disseminated, and the Church of Rome felt the shock thus given to its intellectual supremacy. Pope Urban VIII., though attached to Galileo, and friendly to science, was driven into a position from which he could not recede. The guardian of its faith, he mounted the ramparts of the church to defend the weakest of its bastions, and, with the artillery of the Inquisition, he silenced the batteries of its assailants. The Pope brought the obnoxious work under the eye of the Inquisition, and Galileo, advanced in years, and infirm in health, was summoned before its stern tribunal. He arrived in Rome on the 14th of February 1633, and soon after his arrival he was kindly visited by Cardinal Barberino, the Pope's nephew, and other friends of the church, who, though they felt the necessity of its interference, were yet anxious that it should be done with the least injury to Galileo and to science.
Early in April, when his examination in person took place, he was provided with apartments in the house of the Fiscal of the Inquisition; and to make this nominal confinement as agreeable as possible, his table was provided by the Tuscan ambassador, and his servant was allowed to sleep in an adjoining apartment. Even with these indulgences, however, Galileo could not brook the degradation under which he lay. A return of his complaint ruffled his temper, and made him impatient for his release; and the Cardinal Barberino having been made acquainted with his feelings, liberated the philosopher on his own responsibility, and on the 30th of April, after ten days' confinement, restored him to the hospitable roof of the Tuscan ambassador.
It has been stated on authority which is consideredunquestionable, that during his personal examination Galileo was put to the torture, and that confessions were thus extorted which he had been unwilling to make. He acknowledged that the obnoxious dialogues were written by himself; — that he had obtained a license to print them without informing the functionary who gave it — and that he had been prohibited from publishing such opinions; and in order to excuse himself, he alleged that he had forgotten the injunction under which he lay not to teach, in any manner, the Copernican doctrines. After duly considering the confessions and excuses of their prisoner, the Inquisition appointed the 22d of June as the day on which their sentence was to be pronounced. In obedience to the summons, Galileo repaired to the Holy Office on the morning of the 21st. Clothed in a penitential dress, he was conducted on the 22d to the convent of Minerva, where the Inquisition was assembled, and where an elaborate sentence was pronounced, which will ever be memorable in the history of science. Invoking the name of our Saviour and of the Holy Virgin, Galileo is declared to be a heretic, in consequence of believing that the sun was the centre of the earth's orbit, and did not move from east to west, and defending the opinion that the earth moved and was not the centre of the world. He is therefore charged with having incurred all the censures and penalties enacted against such offences; but from all these he is to be absolved, provided that with a sincere heart, and faith unfeigned, he abjures and curses the heresies he has maintained, as well as every other heresy against the Catholic Church. In order to prevent the recurrence of such crimes, it was also decreed that his work should be prohibited by a formal edict, — that he should be imprisoned during the pleasure of the Inquisition, — and that during the next three years he should recite weekly the seven penitential psalms. This sentence was subscribed by seven cardinals, and on the same day Galileo signed the abjuration which the sentence imposed.
Clothed in the sackcloth of a repentant criminal, Galileo, at the age of seventy, fell upon his knees before the assembled cardinals, and laying his right hand on the Holy Evangelists, he invoked the Divine assistance, in abjuring and detesting and vowing never again to teach the doctrine of the earth's motion and of the sun's stability. He pledged himself never again to propagate such heresies either in his conversation or in his writings, and he vowed that he would observe all the penances which had been inflicted upon him. What a mortifying picture does this scene present to us of moral infirmity and intellectual weakness! If we brand with infamy the unholy zeal of the inquisitorial conclave, what must we think when we behold the venerable sage, whose gray hairs were entwined with the chaplet of immortality, quailing under the fear of man, and sacrificing the convictions of his conscience, and the deductions of his reason, at the altar of a base superstition ? Had Galileo added the courage of the martyr to the wisdom of the sage, — had he carried the glance of his eye round the circle of his judges, and with uplifted hands called upon the living God to witness the truth and immutability of his opinions, he might have disarmed the bigotry of his enemies, and science would have achieved a memorable triumph.
The sentence of abjuration was publicly read at several universities. At Florence it was promulgated in the church of Santa Croce, and the friends and disciples of Galileo were summoned to the ceremonial, in order to witness the degradation of their master. But though thechurch was thus anxious to maintain its authority, Galileo was personally treated with consideration, and even kindness. After remaining only four days in the dungeons of the Inquisition, he was, at the request of the Tuscan ambassador, allowed to reside with him in his palace, and when his health began to suffer, he was permitted to leave Rome and to reside with his friend Piccolomini, Archbishop of Sienna, under whose hospitable roof he completed his investigations respecting the resistance of solids. At the end of six months he was allowed to return to Florence, and before the close of the year he re-entered his house at Arcetri, where he spent the remainder of his days.
Although still a prisoner, Galileo had the happiness of being with his family and living under his own roof; but like the other "spots of azure in his cloudy sky," it was ordained to be of short duration. It was now that he was justly characterized by the poet as "the starry Galileo with his woes." His favourite daughter Maria, who, along with her sister, had joined the convent of St. Matthew, near Arcetri, hastened to the filial duties which she had so long been prevented from discharging. She assumed the task of reciting weekly the seven penitential psalms which formed part of her father's sentence; but she had scarcely commenced her domestic toils when she was seized with a dangerous illness, which in a few weeks proved fatal. Galileo was laid prostrate by this heavy and unexpected blow. He was inconsolable for the loss of his daughter, and disease in various forms shook the frail tenement which philosophy had abandoned. Time, however, the only anodyne of sorrow, produced its usual effects, and Galileo felt himself able to travel to Florence for medical advice. The Pope refused him permission, and he remained at Arcetri from 1634 to 1638, preparing for the press his"Dialogues on Motion," and corresponding with the Dutch government on his proposal to find the longitude by the eclipses of Jupiter's satellites. Galileo, whose eyes had been gradually failing him since 1636, was struck with total blindness in 1638. "The noblest eye," as his friend Father Castelli expressed it, "was darkened — an eye so privileged and gifted with such rare powers, that it may truly be said to have seen more than the eyes of all that are gone, and have opened the eyes of all that were to come." To the want of sight was soon added the want of hearing, and in consequence of the mental labour to which he had been subjected, "his head," as he himself said, "became too busy for his body;" and hypochondriacal attacks, want of sleep, acute rheumatism, and palpitation of the heart, broke down his constitution. His last illness, after two months' continuance, terminated fatally on the 8th January 1642, when he was in the 78th year of his age.
"The scientific character of Galileo," as we have elsewhere had occasion to remark, "and his method of investigating truth, demand our warmest admiration. The number and ingenuity of his inventions, the brilliant discoveries which he made in the heavens, and the depth and beauty of his researches respecting the laws of motion, have gained him the applause of every succeeding age, and have placed him next to Newton in the lists of original and inventive genius. To this high rank he was doubtless elevated by the inductive processes which he followed in all his inquiries. Under the sure guidance of observation and experiment, he advanced to general laws; and if Bacon had never lived, the student of nature would have found in the writings and labours of Galileo not only the boastedprinciples of the Inductive philosophy, but also their practical application to the highest efforts of invention and discovery."
Among the astronomers who preceded Newton in astronomical inquiries, and contributed some ideas to the establishment of the true system of the planets, we must place the names of Bouillaud, Borelli, Hooke, Huygens, Wren, and Halley. After refuting the magnetic notions of Kepler, Bouillaud maintained that the force of attraction must vary reciprocally as the square, and not as Kepler asserted, in the simple ratio of the distance; but Delambre does not allow him any credit in this respect, and remarks that he has done nothing more for astronomy than to introduce the word evection into its language.
The influence of gravity as a central force in the planetary motions has been very distinctly described by Borelli, Professor of Mathematics at Pisa, in his work on the theory of Jupiter's Satellites. He considers the motions of the planets round the sun, and of the satellites round their primaries, as produced by some virtue residing in the central body. In speaking of the motion of bodies in circular orbits, he compares the tendency of the body to recede from the centre of motion to that of a stone whirled in a sling. When this force of recession is equal to the tendency of the body to the centre, a balance is effected between these tendencies, and the body will continually revolve round the centre, and at a determinate distance from it. Delambre attaches no value to these speculations of Borelli. He has in his opinion pointed out no physical cause, and has merely made a series of reflexions which every astronomer would necessarily make who was studying the theory of the satellites. He gives him the credit, however, of being one of the first who conjectured that the comets described round the sun elliptical or parabolic orbits.
The speculations of our distinguished countryman, Dr. Hooke, respecting the cause of the planetary motions, exceeded greatly in originality and value the crude views of Borelli, and form a decided step in physical astronomy. On the 21st of March 1666, he communicated to the Royal Society an account of a series of experiments to determine if bodies experienced any change in their weight at different distances from the surface of the earth "either upwards or downwards." Kepler had maintained that this force, namely, that of gravity, was a property inherent in all celestial bodies, and Hooke proposed "to consider whether this gravitating or attractive power be inherent in the parts of the earth; and if so, whether it be magnetical, electrical, or of some other nature distinct from either." The experiments which he made with the instrument described in this communication, were far from being satisfactory, and he was therefore led to the ingenious idea of measuring the force of gravity "by the motion of a swing clock," which would go slower at the top of a hill than at the bottom.
About two months afterwards, namely, on the 23d May 1666, Hooke communicated to the Society a paper "On the inflexion of a direct motion into a curve by a supervening attractive principle." After maintaining that the celestial bodies moving in circular and elliptical orbits "must have some other cause beside the first impressed impulse to bend their motion into these curves," he considers the only two causes which appear to him capable of producing such an effect. The first of these causes, which he considers an improbable one, is that the tendency to a centre is produced by a greater density of the ether in approaching to the sun. "But the second cause," he adds, "of inflecting a direct motion into a curve may be from an attractive property of the body placed in the centre, whereby it continually endeavours to attract or draw it to itself. For if such a principle be supposed, all the phenomena of the planets seem possible to be explained by the common principle of mechanic motions; and possibly the prosecuting this speculation, may give us a true hypothesis of their motion, and from some few observations their motions may be so far brought to a certainty that we may be able to calculate them to the greatest exactness and certainty that can be desired." After describing the circular pendulum for illustrating these views, he addsthat "by this hypothesis the phenomena of the comets, as well as of the planets, may be solved; and the motions of the secondary as well as of the primary planets. The motions also of the progression of the apsides are very evident, but as for the motion of libration or latitude that cannot be so well made out by this way of pendulum; but by the motion of a wheel upon a point is most easy."
By means of the circular pendulum already mentioned, it was found that "if the impetus of the endeavour by the tangent at the first setting out was stronger than the endeavour to the centre, there was then generated an elliptical motion whose longest diameter was parallel to the direct endeavour of the body in the first point of impulse. But if that impetus was weaker than the endeavour to the centre, there was generated such an elliptical motion whose shorter diameter was parallel to the direct endeavour of the body in the first point of impulse." Another experiment was made by fastening a small pendulous body by a shorter string on the lower part of the wire which suspended the larger ball, "that it might freely make a circular or elliptical motion round about the bigger, whilst the bigger moved circularly or elliptically about another centre." The object of this arrangement was to explain the manner of the moon's motion about the earth; but neither of the balls moved in such perfect circles and ellipses as when they were suspended singly. "A certain point, however, which seemed to be the centre of gravity of the two bodies, however pointed, (considered as one,) seemed to be regularly moved in such a circle or ellipsis, the two balls having other peculiar motions in small epicycles about the same point."<286>
At a later period of his life, Hooke resumed the consideration of the subject of the planetary motions, and, in a work which appeared in 1674, he published some interesting observations on gravity, which we shall give in his own words. — " I shall hereafter," he says, "explain a system of the world differing in many particulars from any yet known, but answering in all things to the common rules of mechanical motions. This depends upon three suppositions : First, That all celestial bodies whatsoever have an attraction or gravitating power towards their own centres, whereby they attract not only their own parts, and keep them from flying from them, as we may observe the Earth to do, but that they also do attract all the other celestial bodies that are within the sphere of their activity, and consequently that not only the Sun and Moon have an influence upon the body and motion of the Earth, and the Earth upon them, but that Mercury, Venus, Mars, Jupiter, and Saturn also, by their attractive powers, have a considerable influence upon its motion, as in the same manner the corresponding attractive power of the Earth hath a considerable influence upon every one of their motions also. The second supposition is this, that all bodies whatsoever that are put into a direct and simple motion, will so continue to move forward in a straight line till they are, by some other effectual powers, deflected, and sent into a motion describing a circle, ellipsis, or some other more compounded curve line. The third supposition is, that these attractive powers are so much the more powerful in operating by how much the nearer the body wrought upon is to their own centres. Now, what these several degrees are, Ihave not yet experimentally verified, but it is a notion which, if fully prosecuted, as it ought to be, will mightily assist the astronomers to reduce all the celestial motions to a certain rule, which I doubt will never be done without it. He that understands the nature of the circular pendulum, and of circular motion, will easily understand the whole of this principle, and will know where to find directions in nature for the true stating thereof. This I only hint at present to such as have ability and opportunity of prosecuting this inquiry, and are not wanting of industry for observing and calculating, wishing heartily such may be found, having myself many other things in hand which I would first complete, and therefore cannot so well attend it. But this I durst promise the undertaker, that he will find all the great motions of the world to be influenced by this principle, and that the true understanding thereof will be the true perfection of astronomy."
In this remarkable passage, the doctrine of universal gravitation, and the general law of the planetary motions, are clearly laid down. The diminution of gravity as the square of the distance, is alone wanting to complete the basis of the Newtonian philosophy; but even this desideratum was in the course of a few years supplied by Dr. Hooke. In a letter which he addressed to Newton in 1679, relative to the curve described by a projectile influenced by the Earth's daily motion, he asserted, that ifthe force of gravity decreased as the square of the distance, the curve described by a projectile would be an ellipse, whose focus was the centre of the Earth. But however great be the merit which we may assign to Hooke's experimental results and sagacious views, they cannot be regarded either as anticipating the discoveries of Newton, or diminishing his fame. Newton had made the same discoveries by independent researches, and there is no reason to believe that he derived any ideas from his contemporaries. <289>
 See Art. Optics in Edin. Encyclopædia, vol. xv. p. 462.
 The Cardinal's letter is published in the work of Copernicus afterwards mentioned.
 These facts are recorded by Copernicus himself in the preface to his work.
 Nicolai Copernici Torinensis De Revolutionibus orbium cœlestium, Lib. vi. Fol. A second edition in folio appeared at Basle in 1566, and a third edition in quarto was published at Amsterdam in 1617, with notes, by Nicolas Muler, under the title of Astronomia Instaurata, &c.
 Copernicus died in 1543, at the age of 70.
 " Neque enim necesse est, eas hypotheses esse veras, imo ne verisimiles quidem, sed sufficit hoc unum, si calculum observationibus congruentem exhibeant." Ad Lectorem.
 Paul III., a member of the Farnese family, who held the Pontificate from 1534 to 1550. The year in which this preface was written is not known.
 Astronomiæ Instauratæ Progymnasmata. 1602.
 Published at the end of the Rudolphine Tables.
 These researches were published in his Prodromus Dissertationum Cosmographicorum, &c. Tubingæ, 1596, 4to.
 Kepler was foiled in his attempt to find out the law of refraction, afterwards discovered by Snellius. His optical discoveries will be found in his Paralipomena ad Vitellionem, Francof. 1604; and in his admirable Dioptrica. Franc. 1611.
 Nova Astronomia seu Physica Celestis tradita Commentariis de Motibus Stellæ Martis. Pragæ, 1609, fol.
 Harmonia Mundi, lib. v. Linzii, 1619, fol.
 Harmonia Mundi, lib. v. Linzii, 1619, fol. p. 178.
 Professor Moll, Journal of Royal Institution, 1831, vol. i. p. 496.
 Sirturus, De Telescopio. Francofurtæ, 1618.
 " Nescio quo fato ductus." — Sidereus Nuncius, p. 20.
 The satellites were observed by our celebrated countryman, Harriot, on the 17th October 1610. — See Martyrs of Science, Life of Galileo, pp. 40, 41.
 See Edinburgh Encyclopædia, Art. Mechanics, vol. xiii. p. 502, where we have given a copious abstract of the mechanical discoveries of Galileo.
 Life of Galileo, chap. vi., in the Martyrs of Science.
 Ismaelis Bullialdi Astronomia Philolaica. — Paris, 1645, p. 23. Sir Isaac admitted that Bullialdus here gives the true "proportion on gravity." — Letter to Halley, June 20, 1686, postscript.
 Theoricæ Mediæorum Planetarum ex causis physicis deuctæ A Alphonso Borellio. — Florentiæ, 1666.
 Newton (in his posthumous work, De Systemate Mundi, § 2, Opera, tom. iii. p. 180, and in his postscript in his letter to Halley, June 20, 1686, where he says "that Borelli did something") and Huygens have attached greater value to the views of Borelli. The last of these philosophers thus speaks of them: — " Refert Plutarchus in libro supramemorato de Facie in Orbe Lunæ, fuisse jam olim qui putaret ideo manere lunam in orbe suo, quod vis recedendi a terra, ob motum circularem, inhiberetur pari vi gravitatis, qua ad terram accedere conaretur. Idemque ævo nostro, non de luna tantum sed et planetis ceteris statuit Alphonsus Borellius, ut nempe primariis eorum gravitas esset solem versus; lunis vero ad Terram Jovem et Saturnum quos comitantur. Multoque diligentius, subtiliusque idem nuper explicuit Isaacus Newtonus, et quomodo ex his causis nascantur Planetarum orbes Elliptici, quos Keplerus excogitaverat ; in quorum foco altero Sol ponitur. Christiani Hugenii Cosmotheoros, lib. ii. ad finem. Opera, tom. ii. p. 720.
 Angelo Fabroni, Lettere inedite d'uomini illustri, tom. i. p. 173.
 Birch's Hist. of Royal Society, vol. ii. pp. 69-72.
 Ibid., vol. ii. pp. 90-92.
 This pendulum consisted of a wire fastened to the roof of the room, with a large wooden ball of lignum vitæ at the end of it. — Waller's Life of Hooke, p. xii.
 Waller's Life of Hooke, p. xii.; and Birch's Hist., vol. ii. p. 92.
 An Attempt to prove the Motion of the Earth from Observations made by Robert Hooke, 4to. See Phil. Trans., No. 101, p. 12.
 In quoting this passage, which Delambre admits to be very curious, we think he scarcely does justice to Hooke, when he says that what it contains is found expressly in Kepler. It is quite true that Kepler mentioned as probable the law of the squares of the distances, but he afterwards, as Delambre admits, rejected it for that of the simple distances. Hooke, on the contrary, announces it as a truth. — See Astronomie du 18me Siècle, pp. 9, 10. Clairaut has justly remarked, that the example of Hooke and Kepler shews how great is the difference between a truth conjectured or asserted, and a truth demonstrated.